In how many ways can we get a sum of at most 17 by throwing six distinct dice ? In how many ways can we get a sum greater than 17 ?

Explanation

To solve the problem of finding the number of ways to get a sum of at most 17 by throwing six distinct dice, and the number of ways to get a sum greater than 17, we can follow these steps:

### Step 1: Understand the Problem
We are throwing six distinct dice, and each die can show a number from 1 to 6. We need to find:
1. The number of ways to get a sum of at most 17.
2. The number of ways to get a sum greater than 17.

### Step 2: Set Up the Variables
...